Recent earthquakes in California (1989 Loma Prieta, 1994 Northridge), Japan (1995 Kobe), Turkey (1999), and Taiwan (1999) have clearly identified the vulnerability of structures to earthquakes and the staggering monetary losses due to such events. Losses from the Northridge earthquake alone are estimated at $15 billion. Kobe earthquake losses are estimated at hundreds of billions of dollars.
The West Coast of the U.S. and the Pacific Northwest States are all susceptible to earthquakes. Discovery of the New Madrid fault poses a great danger to the Midwest region of the U.S.
The Eastern Coast of the U.S. from Florida to Rhode Island is also susceptible to hurricanes. The hurricane season typically lasts from June through November each year. On an average, 12 to 14 hurricanes are generated in the Gulf each year. Losses from these hurricanes are also estimated at hundreds of billions of dollars. Losses from hurricane Andrew alone are estimated at $25 billion.
Although all structures built in these regions are designed according to the national, regional and local building codes, there are catastrophic destructions and failures in these events. To understand why, the building codes need to be analyzed.
Building seismic design forces are customarily provided by the Uniform Building Code (UBC). The UBC is updated from time to time with 1997 UBC being the current version in effect. The UBC states “The purpose of the earthquake provisions herein is primarily to safeguard against major structural failures and loss of life, not to limit damage or maintain function.” The Structural Engineers Association of California (SEAOC) 1996 commentary adds the following to the UBC statement: “ . . . or provide for easy repair.”
The basic design procedure recommended by the Code assumes that the structure will undergo inelastic behavior and will sustain damage, i.e., may be permanently deformed or broken, during a design level earthquake. This is implied by the use of the R-factor in the 1997 UBC, (i.e., “numerical coefficient representative of the inherent overstrength and global ductility capacity of lateral-force-resisting systems”) to reduce the design lateral forces on a structure. A typical design procedure is as follows: 1. selection of a design level earthquake intensity; 2. reduction of the applied forces (e.g., base shear) computed from the design earthquake by a Code recommended R-factor; and 3. design of the structure (using the current practice of linear elastic analyses) for these reduced force levels to ensure elastic response such that the structure assumes its original shape after loading.
For different structure types the maximum R-factors are recommended in the Code. However, the selection of an appropriate factor for the structure under consideration, up to the maximum allowable Code value, is left to the discretion of the designer. Selection of the R-factor is usually determined by the performance criteria the owner wishes to establish. Thus, if the owner wishes the structure to be undamaged for the design level earthquake forces, the designer would select a value of R equal to 1.0. This decision, however, would result in a considerable increase in the cost of the structure and, given the random nature of the earthquake occurrence, this choice is not usually considered to be cost-effective.
A value of the reduction factor, R, greater than approximately 1.5 implies that the system will undergo inelastic behavior and will be damaged if a ground motion of design intensity is observed at the site. The coefficient of 1.5 represents the average factor, which is used in design to either factor the loads in load factor design or factor the yield strength of materials in working stress design. The R-factor is intended to refer to an acceptable level of damage via a global ductility response measure.
Thus, for a working stress design, if a R-factor of 10 is used in the design, the structure is assumed to sustain a global ductility of up to approximately 10/1.5=6.7. Global ductility is a measure of damage. Typically for a building subjected to earthquake motions, it is defined as the ratio of the maximum building roof displacement and the roof displacement at which the first significant damage occurs anywhere in the building. Such assumed ductilities used in design can only be confirmed by a nonlinear analysis (or experimental testing).
It has been widely published in literature that the methodology called “nonlinear analyses, nonlinear dynamics or failure dynamics” utilized in computer programs is the only realistic way to assess damage due to catastrophic events. Over the past 25 years, numerous reports from reputable Universities like U.C. Berkeley, Stanford and others have clearly stated these findings. The oil industry realized the value of such methodology and has incorporated it as a requirement in the API RP 2A Design Code. All offshore structures designed and built in the U.S. must comply with this Code.
Unlike the oil industry's design code, however, the building codes do not require such a state-of-the-art nonlinear analysis to confirm that the assumed global ductilities can be achieved in the adopted design. There are three primary reasons for not enforcing such a requirement in the building codes. First, non-linear analysis is too complex and too expensive to develop and validate for a wide variety of applications. It is important to note that the computational intensity of these algorithms have historically required Cyber mainframe class of computers available through places such as the Lawrence Livermore Laboratory. Second, it requires extensive manual intervention of an engineer with specialized training and theoretical background to set-up input models for a given structure. Third, because typical outputs from these analyses are voluminous, results interpretation is time consuming and requires specialized engineering knowledge.